The angle alpha=-(3pi)/2 means the point (0,1) on the unit circumference (center (0,0) and radius 1). In fact, pi/2 is a quarter of a turn, and you must do three quarters clockwise starting from (1,0).
That being said, remember that cos(alpha) and sin(alpha) are, respectively, nothing but the x and y components of any point laying on the circumference. We easily have cos(-(3pi)/2) = 0, and sin(-(3pi)/2) = 1.
Knowing these values, the others are straightforward:
tan(-(3pi)/2) = \frac{sin(-(3pi)/2)}{cos(-(3pi)/2)} is undefined.
cot(-(3pi)/2) = \frac{cos(-(3pi)/2)}{sin(-(3pi)/2)} = 0/1 = 0
csc(-(3pi)/2) = 1/(sin(-(3pi)/2)) = 1/1 = 1
sec(-(3pi)/2) = 1/(cos(-(3pi)/2)) is undefined.
